Environmental Data Analysis: An Introduction with Examples in R

✍ Scribed by Carsten Dormann

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 277
• Category: Library

✦ Synopsis

Environmental Data Analysis is an introductory statistics textbook for environmental science. It covers descriptive, inferential and predictive statistics, centred on the Generalized Linear Model. The key idea behind this book is to approach statistical analyses from the perspective of maximum likelihood, essentially treating most analyses as (multiple) regression problems. The reader will be introduced to statistical distributions early on, and will learn to deploy models suitable for the data at hand, which in environmental science are often not normally distributed. To make the initially steep learning curve more manageable, each statistical chapter is followed by a walk-through in a corresponding R-based how-to chapter, which reviews the theory and applies it to environmental data. In this way, a coherent and expandable foundation in parametric statistics is laid, which can be expanded in advanced courses.The content has been “field-tested” in several years of courses on statistics for Environmental Science, Geography and Forestry taught at the University of Freiburg.

✦ Table of Contents

Preface
References
The Technical Side: Selecting a Statistical Software
Downloading and Installing R
A Short Test in R
Editors and Environments for R
Tutorial
References
Contents
1 Samples, Random Variables—Histograms, Density Distribution
1.1 Sample Statistics
1.1.1 Measures of Centrality
1.1.2 Measures of Spread
1.1.3 Sample Statistics: An Example
1.2 Frequency, Density and Distribution
References
2 Samples, Random Variables—Histograms and Density Distribution in R
2.1 Data Collection
2.2 Data Entry
2.3 Importing Data to R
2.3.1 Entering Small Data Sets Manually
2.3.2 Read in Larger Data Sets from a File
2.4 Simple, Descriptive Statistics and Graphic Representation
2.4.1 Graphic Representation of Sample Statistics with R
2.4.2 Descriptive Statistics with R
2.4.3 Density Histogram and Empirical Density
2.5 Exercises
References
3 Distributions, Parameters and Estimators
3.1 Distribution
3.1.1 Central Limit Theorem
3.2 Parameters of a Distribution
3.3 Estimators (for Distribution Parameters)
3.3.1 The Likelihood
3.3.2 Maximizing the Likelihood
3.3.3 Maximum Likelihood—Analytical
3.3.4 Maximum Likelihood—Numerical
3.3.5 Maximum Likelihood—High Praise
3.4 Some Important Distributions
3.4.1 Normal (= Gaussian) Distribution
3.4.2 Bernoulli Distribution
3.4.3 Binomial Distribution
3.4.4 Poisson Distribution
3.4.5 Negative Binomial Distribution
3.4.6 Log-Normal Distribution
3.4.7 Uniform Distribution
3.4.8 β-distribution
3.4.9 γ-distribution
3.4.10 Truncated Distributions
3.5 Selecting a Distribution
3.5.1 Comparing Two Distributions: The Kolmogorov-Smirnov Test
3.5.2 Comparing Fits: Likelihood and the Akaike Information Criterion
References
4 Distributions, Parameters and Estimators in R
4.1 Displaying Distributions
4.1.1 Continuous Distributions
4.1.2 Discrete Distributions
4.2 Calculating the Likelihood of a Data Set
4.3 Empirical Cumulative Distribution Function and the Kolmogorov-Smirnov Test
4.4 Test for Normal Distribution
4.5 Exercises
References
5 Correlation and Association
5.1 Correlation
5.1.1 Non-parametric Correlation
5.1.2 Correlation with and between Discrete Variables
5.1.3 Multiple Correlations
5.2 Test for Association—The χ2-test
References
6 Correlation and Association in R
6.1 Non-parametric Correlation
6.2 Multiple Correlations and the Correlation Matrix
6.3 Point-Biserial and Point-Polyserial Correlation
6.4 The χ2-test with R
6.5 Exercises
Reference
7 Regression—Part I
7.1 Regression
7.1.1 Regression: A Distribution Parameter Varies with the Predictor
7.1.2 Regression and Maximum Likelihood
7.1.3 The Other Scale and the Link Function
7.2 Categorical Predictors
7.2.1 A Categorical Predictor with Two Levels
7.2.2 A Categorical Predictor with More that Two Levels
7.3 A Couple of Examples
7.3.1 Height and Sex—A GLM Without The G
7.3.2 Smokers and Sex—The χ2-test as a Binomial GLM
Reference
8 Regression in R—Part I
8.1 Regression Using GLM
8.2 Regression: Maximum Likelihood by Hand
8.2.1 Poisson Model by Hand
8.2.2 Non-linear Regression by Hand
8.3 GLM with VGAM
8.4 Modelling Distribution Parameters (Other Than Just the Mean)
8.5 Exercises
References
9 Regression—Part II
9.1 Model Diagnostics
9.1.1 Analysis of the Predictors
9.1.2 Analysis of Influential Points
9.1.3 Analysis of the Dispersion
9.1.4 Analysis of the Residuals
9.1.5 Analysis of the Functional Relationship Between y and x
References
10 Regression in R—Part II
10.1 Model Diagnostics
10.1.1 Analysis of the Predictors
10.1.2 Analysis of Influential Points
10.1.3 Analysis of the Dispersion
10.1.4 Analysis of the Residuals
10.1.5 Analysis of the Functional Relationship Between y and x
10.2 Regression Diagnostics for a Linear Model (LM)
10.3 Exercises
References
11 The Linear Model: t-test and ANOVA
11.1 The t-test
11.1.1 One Sample t-test
11.1.2 Paired Sample t-test
11.1.3 Two Sample Test
11.2 Analysis of Variance (ANOVA): Analysing for Significant Differences
11.2.1 ANOVA with a Continuous Predictor: An Example
11.2.2 Assumptions of an ANOVA
11.2.3 Making Non-normally Distributed Data Work with ANOVA
11.2.4 ANOVA for More Than 2 Levels
11.2.5 Post-Hoc Comparisons
11.3 From Regression to ANOVA
11.3.1 ANOVA and Regression: Comparing Results
11.3.2 Degrees of Freedom from ANOVA and Explaining Them Through Regression
11.4 ANOVAs for GLMs
References
12 The Linear Model: t-test and ANOVA in R
12.1 t-test and Its Variants in R
12.2 ANOVA in R
12.2.1 Test for Homogeneity of Variance
12.2.2 Calculate Significance from F-values
12.2.3 Post-Hoc Comparisons with R
12.3 ANOVA to Regression and Back
12.4 ANOVAs for GLM
12.5 Exercises
13 Hypotheses and Tests
13.1 Scientific Method: Observations …
13.2 Testing Hypotheses
13.2.1 Recipe for Testing Hypotheses
13.2.2 Error Types
13.3 Tests
13.3.1 Further Test Related Terminology
13.3.2 Final Comments on Tests
13.4 Exercises
References
14 Experimental Design
14.1 Design Principles
14.1.1 Principle 1: Representativity
14.1.2 Principle 2: Independence
14.1.3 Principle 3: Control Group
14.2 Important Designs for Manipulative Experiments
14.2.1 Fully Randomised Block Design
14.2.2 Split-Plot Design
14.2.3 Nested Design
14.3 Survey Design
14.3.1 Simple Random Sampling
14.3.2 Multi-level Sampling Methods
References
15 Multiple Regression: Regression with Multiple Predictors
15.1 Visualising Multiple Predictors
15.1.1 Visualising Two Categorical Predictors
15.1.2 Visualising a Categorical and a Continuous Predictor
15.2 Interactions Between Predictors
15.3 Collinearity
15.3.1 Principal Component Analysis
15.3.2 Cluster Analysis
15.4 Model Selection
15.4.1 Two-Way ANOVA by Hand
15.5 For the Math Curious: The Math Behind the Linear Model
References
16 Multiple Regression in R
16.1 Visualising and Fitting Interactions
16.1.1 Two Categorical Predictors: Regression and ANOVA
16.1.2 One Continuous and One Categorical Predictor
16.1.3 Multiple Regression with Two Continuous Variables
16.2 Collinearity
16.2.1 Principal Component Analysis in R
16.2.2 Cluster-Analysis in R
16.3 Model Selection
16.3.1 Model Selection by Hand
16.3.2 Automated Model Selection
16.3.3 Best-Subset Regression
16.4 Exercises
References
17 Outlook
References
Index